Results 1 to 3 of 3

Math Help - Question on linear transformaiton

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    12

    Question on linear transformaiton

    Let V and W be vector spaces over F field, dimV=n, and dim W=m. What is the dimension of the vector space L(V,W), and what is an optional basis?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Question on linear transformaiton

    Quote Originally Posted by noricka View Post
    Let V and W be vector spaces over F field, dimV=n, and dim W=m. What is the dimension of the vector space L(V,W), and what is an optional basis?
    Hint : If we fix B_V and B_W basis of V and W respectively, there is a natural isomorphism \phi:\mathcal{L}(V,W)\to \mathbb{K}^{m \times n} given by \phi (T)=[T]_{B_V}^{B_W} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,284
    Thanks
    673

    Re: Question on linear transformaiton

    you may also wish to consider E_{i,j} \in \mathcal{L}(V,W) : E_{i,j}(a_1v_1+a_2v_2+\dots+a_nv_n) = a_jw_i.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra: Linear Independence question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 3rd 2011, 05:28 AM
  2. Linear Map Question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 18th 2011, 01:40 AM
  3. Linear ODE question
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 25th 2010, 08:19 PM
  4. Linear Algebra Question - Linear Operators
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 3rd 2009, 04:33 AM
  5. Linear question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 16th 2007, 06:40 AM

Search Tags


/mathhelpforum @mathhelpforum